simplify this...1?

Question

2n^1/3 (n^2/3 + n^ -1/3)


The 1st letter n has an exponent of 1/3
The 2nd letter n has an exponent of 2/3
The 3rd letter n has an exponent of -1/3

Answer 1

2n+2
...or....
2(n+1)

whichever you prefer
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2n^1/3 (n^2/3 + n^ -1/3) =
2n^(1/3+2/3) + 2n^(-1/3+1/3) =
2n^(1) + 2n^(0) =
2n+2 or 2(n+1)

Answer 2

You need to use the following law of indices: a^p * a^q = a^(p+q)

So multiplying out the brackets we get:

2n^(1/3 + 2/3) + 2n^(1/3 - 1/3)
= 2n^1 + 2n^0
= 2n + 2 (since n^0 = 1)

So the final answer is 2n+2 or 2(n+1) if you prefer.

Answer 3

Well, do the distribution and you get:

2n^(1/3)n^(2/3) + 2n^(1/3)n^(-1/3)

Then follow the rule about adding exponents to multiply, and you get

2n^1 + 2n^0 = 2n + 2

Answer 4

2n^1/3 (n^2/3 + n^ -1/3)
=2n+2n^0
=2n+2
=2(n+1)

Answer 5

2n^1/3 (n^2/3 + n^ -1/3)
= 2n^(1/3 +2/3) + 2n^(1/2-1/3)
= 2n^1 + 2n ^0
=2n+2
=2(n+1)

Answer 6

2n^1/3 (n^2/3 + n^ -1/3)
= (2n^1/3)(n^2/3) + (2n^1/3)(n^ -1/3)
= 2n^(1/3+2/3) + 2n^(1/3-1/3)
=2n^1 + 2n^0
=2n + 2

Answer 7

After you get your final grade, look back on how you were spoon fed, and ask yourself, "Gee, why did I get such a lousy grade?"